ES204
Mechanical Vibrations
Dr. Cornwell
C217
x8232 (office), 466-5303 (home)
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Today’s Objectives:
Students will:
In-Class Activities:
a) Understand my background
in vibrations
• Mini-lecture on
vibrations
b) Understand what they are
expected to know from
ES205
c) Modeling of vibrating
systems
• Group discussion on
applications
• Mini-lecture on
modeling
• Example
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Administrative Information
•
•
•
•
Homework (discussed on next slide)
Two exams and a final
Paper on contemporary issues
Labs (still to be determined)
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Homework Information
General Comments
• Do the homework daily!
• Due dates in the course outline.
• The homework should be written up according to the instructions
contained in the “Homework Format” page of the administrative
handout.
• Include units, Maple printouts, define system, etc. (Same as SEC)
• Late homework will not be accepted except for medical reasons or the
student has received prior approval from me.
• 10% is very deceptive
Getting Help
• Get help from your classmates (but do not copy) - copying in anyway
is forbidden
• Get help from me
Honor Statement required
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
I’ve done a lot of vibrations work at LANL
• Vibration Analysis and Testing
–
–
–
–
Lunar Prospector
Bridge columns at UC-Irvine
Fetchin Institute
NIF
• Structural Health Monitoring
– Alamosa Canyon Bridge
– LADSS
• Power Harvesting
• Hip Implant monitoring
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Alamosa Canyon Bridge Test
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Enhancing Power Harvesting Using a
Tuned Auxiliary Structure
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Femoral Component Insertion Monitoring Using
Human Cadaveric Specimens
Andrew Crisman, Rose-Hulman Institute of Technology
Molly McCuskey, University of New Mexico
Nathanael Yoder, Harvey Mudd College
Phillip Cornwell, Rose-Hulman Institute of Technology
R. Michael Meneghini, St. Vincent Center for Joint Replacement
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Hip arthroplasty involves several steps
Hip Socket
Femoral
Head
Osteoarthritis
Femur
Vibrations
LADSS
Rose-Hulman Institute of Technology
3 Engineering
Mechanical
Source: www.webmd.com/DW/arthritis/aa14678.asp (Jul 2004)
A test structure was
constructed for the testing
simulated femurs
(sawbones)
Vibrations
LADSS
Rose-Hulman Institute of Technology
4 Engineering
Mechanical
Cadavers were recently tested at UCSD
surgery used
clamps
and
TheInsurgeon
larger
retractors
are used
incisions
at UCSD
Vibrations
LADSS
Rose-Hulman Institute of Technology
13 Engineering
Mechanical
Things you should get out of this class
• Good understanding of SDOF systems
– Terminology
– Systems ID
– Free response
– Harmonic excitation
• MDOF System free and force response (no
damping)
– Natural frequencies and modes
• Vibration mitigation (isolators, absorbers)
• Improved Matlab skills.
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Introduction to Vibrations
“The study of oscillatory motions of bodies and the forces
associated with them”
The system includes:
• Means for storing potential energy (
• Means for storing kinetic energy (
• Means by which energy is gradually lost (
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
)
)
)
Turn to your neighbor and discuss:
What are some of the positive and negative results/applications of
vibrations
1.
2.
3.
4.
Vibrations is important in the design of ...
1.
2.
3.
4.
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Vibrations can be good or bad
Good:
• Conveyors, hoppers,
compactors
• Mechanical shakers,
mixers, sieves, sorters, etc.
• Musical instruments
• Structural health
monitoring
• etc.
Bad
• RESONANCE!
– Machine tools, vehicles,
turbines, pumps,
compressors, buildings,
aircraft, etc.
• Excessive vibrations leads
to loosening of parts,
noise, wear
• Effects on human body
include discomfort,
fatigue, loss of efficiency
• etc.
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
There are lots of applications
Condition
monitoring
Model
updating
Noise and
vibrations
control
Sports
equipment
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
What you should know from ES205
• Modeling
– Equivalent springs, masses
• Finding equations of motion (drawing FBDs and
applying principles)
• Response of SDOF systems
– Step response
– Harmonic forcing
• Bode plots
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Definitions
Degree of Freedom (DOF) – the minimum number of coordinates required to
completely determine the positions of all parts of a system.
Discrete System – A system that can be described by a finite number of DOF.
Continuous System – A system that can only be described by an infinte number
of DOF.
Rigid body in
space
# DOF =
# DOF =
Assume
planar motion
# DOF =
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Cantilevered beam
# DOF =
Classification
1.
SDOF
vs.
MDOF
SEP
SEP
x1
x
SEP
x
2
SEP
x3
2.
Free vibration vs. Forced vibration
•
•
Free vibration – after an initial disturbance, the system is left to
vibrate on its own
Forced vibration – the system is subjected to an external force
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
Classification (cont.)
3. Undamped vs. Damped
1
1.5
0.8
1
0.6
0.5
x
0.4
x0.2
0
0
1
2
3
-0.5
4
t
5
0
0
1
2
3
-0.2
4
t
-0.4
-1
-0.6
-1.5
Damped
Undamped
Types of Damping:_____________________________________
Note: Damping ≠ Dampening
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
5
Classification (cont.)
• Linear vs. Nonlinear
– Linear: all the components behave linearly
– Nonlinear: any of the basic components behave
non-linearly
or
• Deterministic vs. Random Vibrations
– Deterministic: Can predict the response of the
system. The excitation force is know exactly
– Random: Only the statistics of the excitation
are known. The response can only be described
in statistical terms. Examples include road
roughness or earthquake loading
Vibrations
Rose-Hulman Institute of Technology
Mechanical Engineering
1.5
1
or
0.5
x
0
0
-0.5
-1
-1.5
1
2
3
4
t
5